A graph is \(k\) -planar if it has a drawing in the plane so
that each edge is crossed by at most \(k\)  edges. It is
fan-crossing free if the crossing edges are independent,
i.e., they have distinct vertices,
and fan-crossing if the crossing edges have a common
vertex, i.e., they form a fan.
A drawing of a graph is
\(k\) -quasi-planar if \(k\)  edges do not mutually cross.
3-quasi-planar graphs are called quasi-planar, see
Fig. REF . The aforementioned graphs can also be defined
by first order logic formulas [1]} and in terms of an
avoidance of (natural and radial) grids [2]}. A
drawing is \(k\) -gap-planar [3]} if each crossing
is assigned to an edge involved in the crossing so that at most \(k\) 
crossings are assigned to each edge. Then every \(2k\) -planar drawing
is \(k\) -gap-planar [3]}. These properties are
topological. They hold for embeddings, which are equivalence classes
of topologically equivalent drawings.
Right angle crossing (RAC) is a geometric property, in which the edges are drawn straight line
and may cross at a right angle [5]}.
<FIGURE>